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Filinov AV, Bonitz M. Equation of state of partially ionized hydrogen and deuterium plasma revisited. Phys Rev E 2023; 108:055212. [PMID: 38115427 DOI: 10.1103/physreve.108.055212] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/04/2023] [Accepted: 10/31/2023] [Indexed: 12/21/2023]
Abstract
We present improved first-principle fermionic path integral Monte Carlo (PIMC) simulation results for a dense partially ionized hydrogen (deuterium) plasma, for temperatures in the range 15000K≤T≤400000K and densities 7×10^{-7}g/cm^{3}≤ρ_{H}≤0.085g/cm^{3} (1.4×10^{-6}g/cm^{3}≤ρ_{D}≤0.17g/cm^{3}), corresponding to 100≥r_{s}≥2, where r_{s}=r[over ¯]/a_{B} is the ratio of the mean interparticle distance to the Bohr radius. These simulations are based on the fermionic propagator PIMC (FP-PIMC) approach in the grand canonical ensemble [Filinov et al., Contrib. Plasma Phys. 61, e202100112 (2021)0863-104210.1002/ctpp.202100112] and fully account for correlation and quantum degeneracy and spin effects. For the application to hydrogen and deuterium, we develop a combination of the fourth-order factorization and the pair product ansatz for the density matrix. Moreover, we avoid the fixed node approximation that may lead to uncontrolled errors in restricted PIMC (RPIMC). Our results allow us to critically reevaluate the accuracy of the RPIMC simulations for hydrogen by Hu et al. [Phys. Rev. B 84, 224109 (2011)1098-012110.1103/PhysRevB.84.224109] and of various chemical models. The deviations are generally found to be small, but for the lowest temperature, T=15640 K they reach several percent. We present detailed tables with our first principles results for the pressure and energy isotherms. We expect our updated results will serve as a valuable benchmark for comparison with other methods.
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Affiliation(s)
- A V Filinov
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
| | - M Bonitz
- Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, Leibnizstraße 15, 24098 Kiel, Germany
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Danel JF, Kazandjian L, Piron R. Equation of state of warm dense deuterium and its isotopes from density-functional theory molecular dynamics. Phys Rev E 2016; 93:043210. [PMID: 27176421 DOI: 10.1103/physreve.93.043210] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2015] [Indexed: 06/05/2023]
Abstract
Of the two approaches of density-functional theory molecular dynamics, quantum molecular dynamics is limited at high temperature by computational cost whereas orbital-free molecular dynamics, based on an approximation of the kinetic electronic free energy, can be implemented in this domain. In the case of deuterium, it is shown how orbital-free molecular dynamics can be regarded as the limit of quantum molecular dynamics at high temperature for the calculation of the equation of state. To this end, accurate quantum molecular dynamics calculations are performed up to 20 eV at mass densities as low as 0.5g/cm^{3} and up to 10 eV at mass densities as low as 0.2g/cm^{3}. As a result, the limitation in temperature so far attributed to quantum molecular dynamics is overcome and an approach combining quantum and orbital-free molecular dynamics is used to construct an equation of state of deuterium. The thermodynamic domain addressed is that of the fluid phase above 1 eV and 0.2g/cm^{3}. Both pressure and internal energy are calculated as functions of temperature and mass density, and various exchange-correlation contributions are compared. The generalized gradient approximation of the exchange-correlation functional, corrected to approximately include the influence of temperature, is retained and the results obtained are compared to other approaches and to experimental shock data; in parts of the thermodynamic domain addressed, these results significantly differ from those obtained in other first-principles investigations which themselves disagree. The equations of state of hydrogen and tritium above 1 eV and above, respectively, 0.1g/cm^{3} and 0.3g/cm^{3}, can be simply obtained by mass density scaling from the results found for deuterium. This ab initio approach allows one to consistently cover a very large domain of temperature on the domain of mass density outlined above.
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Affiliation(s)
- J-F Danel
- CEA, DAM, DIF, F-91297 Arpajon, France
| | | | - R Piron
- CEA, DAM, DIF, F-91297 Arpajon, France
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Becker A, Lorenzen W, Fortney JJ, Nettelmann N, Schöttler M, Redmer R. AB INITIO EQUATIONS OF STATE FOR HYDROGEN (H-REOS.3) AND HELIUM (He-REOS.3) AND THEIR IMPLICATIONS FOR THE INTERIOR OF BROWN DWARFS. ACTA ACUST UNITED AC 2014. [DOI: 10.1088/0067-0049/215/2/21] [Citation(s) in RCA: 92] [Impact Index Per Article: 9.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Redmer R, Holst B. Metal–Insulator Transition in Dense Hydrogen. METAL-TO-NONMETAL TRANSITIONS 2010. [DOI: 10.1007/978-3-642-03953-9_4] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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Gu YJ, Chen QF, Cai LC, Chen ZY, Zheng J, Jing FQ. Multishock comparison of dense gaseous H[sub 2]+He mixtures up to 30 GPa. J Chem Phys 2009; 130:184506. [DOI: 10.1063/1.3124562] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Chen QF, Cai LC, Zhang Y, Gu YJ. The dissociation and equation of state of dense fluid oxygen at high pressures and high temperatures. J Chem Phys 2008; 128:104512. [DOI: 10.1063/1.2837480] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jakob B, Reinhard PG, Toepffer C, Zwicknagel G. Wave packet simulation of dense hydrogen. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:036406. [PMID: 17930350 DOI: 10.1103/physreve.76.036406] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/15/2007] [Revised: 05/31/2007] [Indexed: 05/25/2023]
Abstract
Dense hydrogen is studied in the framework of wave packet molecular dynamics. In this semiquantal many-body simulation method the electrons are represented by wave packets which are suitably parametrized. The equilibrium properties and time evolution of the system are obtained with the help of a variational principle. At room temperature the results for the isotherms are in good agreement with anvil experiments. At higher densities beyond the range of the experimental data a transition from a molecular to a metallic state is predicted. The wave packets become delocalized and the electrical conductivity increases sharply. The phase diagram is calculated in a wide range of the pressure-density-temperature space. The observed transition from the molecular to metallic state is accompanied by an increase in density in agreement with recent reverberating shock wave experiments.
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Affiliation(s)
- B Jakob
- Institut für Theoretische Physik II, Universität Erlangen-Nürnberg, Staudtstrasse 7, D-91058 Erlangen, Germany
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Schmidt M. Fundamental measure density functional theory for nonadditive hard-core mixtures: the one-dimensional case. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:031202. [PMID: 17930234 DOI: 10.1103/physreve.76.031202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2007] [Indexed: 05/25/2023]
Abstract
We treat a one-dimensional binary mixture of hard-core particles that possess nonadditive diameters. For this model, a density functional theory is constructed following similar principles as an earlier extension of Rosenfeld's fundamental measure theory to three-dimensional nonadditive hard-sphere mixtures. The theory applies to arbitrary positive and moderate negative nonadditivity and reduces to Percus' exact functional in the additive case. Bulk direct correlation functions are obtained as functional derivatives of the excess free energy functional. Results for the partial pair correlation functions in bulk, as calculated via the Ornstein-Zernike route and using the direct correlation functions as input, show very good agreement with results from our Monte Carlo computer simulations of the mixture.
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Affiliation(s)
- Matthias Schmidt
- H. H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom
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Redmer R, Holst B, Juranek H, Nettelmann N, Schwarz V. Equation of state for dense hydrogen and helium: application to astrophysics. ACTA ACUST UNITED AC 2006. [DOI: 10.1088/0305-4470/39/17/s26] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Schwarz V, Juranek H, Redmer R. Noble gases and hydrogen at high pressures. Phys Chem Chem Phys 2005; 7:1990-5. [DOI: 10.1039/b501476j] [Citation(s) in RCA: 18] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Bezkrovniy V, Filinov VS, Kremp D, Bonitz M, Schlanges M, Kraeft WD, Levashov PR, Fortov VE. Monte Carlo results for the hydrogen Hugoniot. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:057401. [PMID: 15600800 DOI: 10.1103/physreve.70.057401] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2004] [Indexed: 05/24/2023]
Abstract
We propose a theoretical Hugoniot relation obtained by combining results for the equation of state from the direct path integral Monte Carlo technique (DPIMC) and those from reaction ensemble Monte Carlo (REMC) simulations. The main idea of this proposal is based on the fact that the DPMIC technique provides first-principle results for a wide range of densities and temperatures including the region of partially ionized plasmas. On the other hand, for lower temperatures where the formation of molecules becomes dominant, DPIMC simulations become cumbersome and inefficient. For this region it is possible to use accurate REMC simulations where bound states (molecules) are treated on the Born-Oppenheimer level. The remaining interaction is then reduced to the scattering between neutral particles which is reliably treated classically by applying effective potentials. The resulting Hugoniot is located between the experimental values of Knudson et al. [Phys. Rev. Lett. 87, 225501 (2001)] and Collins et al. [Science 281, 1178 (1998)].
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Affiliation(s)
- V Bezkrovniy
- Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, Domstrasse 10a, D-17487, Greifswald, Germany
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Bezkrovniy V, Schlanges M, Kremp D, Kraeft WD. Reaction ensemble Monte Carlo technique and hypernetted chain approximation study of dense hydrogen. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:061204. [PMID: 15244551 DOI: 10.1103/physreve.69.061204] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2003] [Indexed: 05/24/2023]
Abstract
In spite of the simple structure of hydrogen, up to now there is no unified theoretical and experimental description of hydrogen at high pressures. Recent results of Z-pinch experiments show a large deviation from those obtained by laser driven ones. Theoretical investigations including ab initio computer simulations show considerable differences at such extreme conditions from each other and from experimental values. We apply the reaction ensemble Monte Carlo technique on one hand and a combination of the hypernetted chain approximation with the mass action law on the other to study the behavior of dense hydrogen at such conditions. The agreement between both methods for the equation of state and for the Hugoniot curve is excellent. Comparison to other methods and experimental results is also performed.
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Affiliation(s)
- V Bezkrovniy
- Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald, Domstrasse 10a, D-17487 Greifswald, Germany
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Knaup M, Reinhard PG, Toepffer C, Zwicknagel G. Wave packet molecular dynamics simulations of warm dense hydrogen. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/22/344] [Citation(s) in RCA: 37] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Juranek H, Schwarz V, Redmer R. Equation of state for hydrogen and helium in the chemical picture. ACTA ACUST UNITED AC 2003. [DOI: 10.1088/0305-4470/36/22/346] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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